def mystery(x):
if not (isinstance(x, int) and 10**8 <= x < 10**9):
return False
v = [int(str(x)[i:i+3]) for i in range(0, 9, 3)]
if len(set(v)) != 3 or sum(v) != 999:
return False
return all(v[i] == (v[i-1] * v[i-2]) % (sum(v) + 1) for i in range(3))
def mystery(x):
s = str(x)
if len(s) != 5:
return False
if any(not (33 <= ord(c) <= 126) for c in s):
return False
h = 0
for ch in s:
h = (h * 131 + ord(ch)) % 1000003
g = 0
for ch in s[::-1]:
g = (g * 97 + (ord(ch) ^ 0x55)) % 8191
w = sum((i + 1) * (ord(ch) - 31) for i, ch in enumerate(s))
return h == 164706 and g == 3018 and w == 599
def mystery(x):
if not isinstance(x, str) or len(x) != 6:
return False
a = [ord(c) for c in x]
if any(not (32 <= c <= 126) for c in a):
return False
b = sum(a)
c = sum(i * v for i, v in enumerate(a, 1))
d = 0
for v in a:
d ^= v
e = sum(v ^ 13 for v in a)
f = sum(v**2 for v in a)
return b == 629 and c == 2242 and d == 19 and e == 653 and f == 66231
def mystery(x):
if type(x) is not str or len(x) != 8:
return False
if not (x[0].isupper() and x[1].isdigit() and x[2].islower() and x[3].isupper()
and x[4].isdigit() and x[5:].islower()):
return False
z = x[::-1]
z = ''.join(chr(32 + ((ord(ch) - 32 + 7 + 3*i) % 95)) for i, ch in enumerate(z))
z = ''.join(z[i+1] + z[i] for i in range(0, 8, 2))
if z != "myEr+TjI":
return False
a = [ord(c) for c in x]
return (
sum(a) == 674 and
sum(a[::2]) == 346 and
sum(a[1::2]) == 328 and
(a[0] ^ a[1] ^ a[2] ^ a[3] ^ a[4] ^ a[5] ^ a[6] ^ a[7]) == 10
)
def mystery(x):
if not isinstance(x, str) or len(x) != 8:
return False
a = [ord(c) for c in x]
if any(v < 32 or v > 126 for v in a):
return False
# A bitwise dependency chain where each character's ASCII value is linked
# to the previous one in a non-linear way.
b = [(a[i] << 1) ^ (a[i-1] if i > 0 else 85) for i in range(8)]
if b != [61, 200, 148, 61, 138, 209, 249, 241]:
return False
# A polynomial hash to further constrain the sequence.
c = 0
for v in a:
c = (c * 31 + v) % 1000000007
# Final checks for mathematical consistency and to ensure a unique solution.
return c == 866903359 and sum(v**2 for v in a) == 61668
def mystery(x):
if type(x) is not str or len(x) != 12:
return False
if any(not (32 <= ord(ch) <= 126) for ch in x):
return False
a = [ord(ch) - 32 for ch in x]
p = [5, 1, 11, 3, 9, 0, 7, 2, 10, 4, 8, 6]
u = [(a[p[i]] + 17 * i + 29) % 95 for i in range(12)]
v = u[4:8] + u[:4] + u[8:]
return (
''.join(chr(32 + n) for n in v) == ":d5POeKqjEJ=" and
sum(a) == 445 and
sum((i + 1) * a[i] for i in range(12)) == 2844
)
def mystery(x):
if not isinstance(x, str) or len(x) != 8:
return False
a = [ord(c) for c in x]
if any(v < 32 or v > 126 for v in a):
return False
# Construct a 4x4 symmetric matrix for a linear transformation
m = [[(i*k + i + k + 2) % 11 for k in range(4)] for i in range(4)]
# Apply Hill-cipher-like linear transformation modulo 127
res = []
for block in [a[:4], a[4:]]:
for i in range(4):
val = sum(m[i][j] * block[j] for j in range(4)) % 127
res.append(val)
# Validate against target transformed values
if res != [20, 33, 45, 96, 51, 67, 126, 47]:
return False
# Checksum constraints to ensure a unique solution
s1 = sum(a)
s2 = sum((i + 1) * v for i, v in enumerate(a))
s3 = sum(v**2 for v in a)
s4 = 0
for v in a:
s4 ^= v
return s1 == 804 and s2 == 3725 and s3 == 82272 and s4 == 36
def mystery(x):
if type(x) is not str or len(x) != 7:
return False
a = [ord(c) for c in x]
if any(v < 65 or v > 90 for v in a):
return False
if len(set(a)) != 7:
return False
h1 = 0
for v in a:
h1 = (h1 * 257 + v) % 10000019
h2 = 0
for v in a[::-1]:
h2 = (h2 * 263 + (v ^ 0x3D)) % 1000033
return (
h1 == 9845382 and
h2 == 260296 and
sum(a) == 476 and
sum((i + 1) * v for i, v in enumerate(a)) == 1932 and
(a[0] ^ a[1] ^ a[2] ^ a[3] ^ a[4] ^ a[5] ^ a[6]) == 64 and
sum(v * v for v in a) == 32396
)
def mystery(x):
if not isinstance(x, str) or len(x) != 9:
return False
a = [ord(c) for c in x]
if any(not (32 <= v <= 126) for v in a):
return False
# This puzzle involves a cyclic bitwise transformation.
# Each character's ASCII value is left-rotated by 3 bits
# (within an 8-bit byte) and then XORed with the ASCII
# value of the next character in the string.
r = [(((a[i] << 3) | (a[i] >> 5)) & 0xFF) ^ a[(i + 1) % 9] for i in range(9)]
if r != [251, 191, 203, 115, 239, 82, 59, 162, 201]:
return False
# Standard algebraic and hash-based integrity checks.
s = sum(a)
w = sum((i + 1) * v for i, v in enumerate(a))
q = sum(v**2 for v in a)
h = 0
for v in a:
h = (h * 31 + v) % 1000000007
return s == 713 and w == 3076 and q == 65907 and h == 284299081
def mystery(x):
if type(x) is not int or not (10**11 <= x < 10**12):
return False
d = [int(c) for c in f"{x:012d}"]
p = [9, 2, 5, 8, 11, 0, 3, 6, 1, 4, 7, 10]
u = [d[i] for i in p]
v = [(3 * u[i] + u[i - 2] + i) % 10 for i in range(12)]
z = [(v[(i + 3) % 12] + 7 * v[11 - i] + 2 * i) % 10 for i in range(12)]
return (
tuple(z) == (9, 2, 5, 7, 6, 1, 1, 2, 1, 7, 4, 9)
and sum(d) == 52
and sum((i + 1) * d[i] for i in range(12)) == 388
and sum(v) == 64
and sum(v[i] * v[(i + 1) % 12] for i in range(12)) == 334
and sum(vv * vv for vv in d) == 296
and (d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[6] ^ d[7] ^ d[8] ^ d[9] ^ d[10] ^ d[11]) == 4
and sum((i + 1) * z[i] for i in range(12)) == 346
)